Minimal order nonlinear observer for leak detection

A method for leaks location in a pipeline, using sensors only at the extremes of the line is presented. The detection problem is solved, assuming a nonlinear fluid model of finite dimension with uncertainty in the leak position, and generating the residual with two minimal order nonlinear observers. Flow and pressure data at the beginning and at end of the line are considered as output and input of the system respectively. Since the proposed model satisfies (1) the condition to generate a residual, assuming at the most two leaks, and (2) the strong detectability fault property,for each output component, two nonlinear robust filters with respect to a leak are designed to generate the residual. To simplify the residual evaluation and estimate the leak position, a static relationship between each component of the residual and the position error is derived. The main contribution of this paper is to take advantage of the residual equation with uncertainty to isolate a fault. The effectiveness of this approach is shown by a comparison with the practical method reported in [1] using results obtained from simulated and experimental data of a water pilot pipeline of 132 m long, with a diameter of 0.1 In and with a flow rate of 12 l/s.